Tight contact structures on some bounded Seifert manifolds with minimal convex boundary

We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds N=M(D ²;r ₁,r ₂) with minimal convex boundary of slope s and Giroux torsion 0 along ?N, where r ₁,r ₂∈(0,1)∩?, in the following cases: (1) s∈(?∞,0)∪[2,+∞); (2) s∈[0,1) and r ₁,r ₂∈[1/2,1); (3) s∈[1,2) and $r_{1},r_{2}in left(0,frac{1}{2}right)$ ; (4) s=∞ and $r_{1}=r_{2}=frac{1}{2}$ . We also classify positive tight contact structures, up to isotopy fixing the boundary, on $M left(D^{2};frac{1}{2},frac{1}{2}right)$ with minimal convex boundary of arbitrary slope and Giroux torsion greater than 0 along the boundary.